MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Identify test statistic

Identify p-value

Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.__<μ1−μ2<__​(Round to three decimal places as​ needed.)

### Educational Text on Hypothesis Testing

**Context:**

Listed in the data table are IQ scores for a random sample of subjects with medium lead levels in their blood. Also included are statistics from a study on IQ scores for a random sample of subjects with high lead levels. Assume that the two samples are independent simple random samples from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) and (b) below.

**Instructions:**

**a. Use a 0.01 significance level to test the claim:**  
The mean IQ score for subjects with medium lead levels is higher than the mean score for subjects with high lead levels.

**Determine the null and alternative hypotheses:** 

Assume that:
- Population 1 consists of subjects with medium lead levels.
- Population 2 consists of subjects with high lead levels.

**Hypothesis Options:**

- **A.**  
  \( H_0: \mu_1 = \mu_2 \)  
  \( H_1: \mu_1 \neq \mu_2 \)  

- **B.**  
  \( H_0: \mu_1 = \mu_2 \)  
  \( H_1: \mu_1 > \mu_2 \)  

- **C.**  
  \( H_0: \mu_1 \neq \mu_2 \)  
  \( H_1: \mu_1 = \mu_2 \)  

- **D.**  
  \( H_0: \mu_1 \leq \mu_2 \)  
  \( H_1: \mu_1 > \mu_2 \)  

**Correct Answer:**
**B.**   
\( H_0: \mu_1 = \mu_2 \)  
\( H_1: \mu_1 > \mu_2 \)  

**Note:**

- The null hypothesis (\( H_0 \)) suggests no difference in means.
- The alternative hypothesis (\( H_1 \)) suggests that the mean IQ score for subjects with medium lead levels is greater than for those with high lead levels.

**Test Statistic:**
Calculate the test statistic. (Round to two decimal places as needed.)

**Visual Element:**

- The image includes options for indicating null and alternative hypotheses, with option B being correctly marked. There is also a placeholder for calculating the
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Transcribed Image Text:### Educational Text on Hypothesis Testing **Context:** Listed in the data table are IQ scores for a random sample of subjects with medium lead levels in their blood. Also included are statistics from a study on IQ scores for a random sample of subjects with high lead levels. Assume that the two samples are independent simple random samples from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. **Instructions:** **a. Use a 0.01 significance level to test the claim:** The mean IQ score for subjects with medium lead levels is higher than the mean score for subjects with high lead levels. **Determine the null and alternative hypotheses:** Assume that: - Population 1 consists of subjects with medium lead levels. - Population 2 consists of subjects with high lead levels. **Hypothesis Options:** - **A.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) - **B.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 > \mu_2 \) - **C.** \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 = \mu_2 \) - **D.** \( H_0: \mu_1 \leq \mu_2 \) \( H_1: \mu_1 > \mu_2 \) **Correct Answer:** **B.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 > \mu_2 \) **Note:** - The null hypothesis (\( H_0 \)) suggests no difference in means. - The alternative hypothesis (\( H_1 \)) suggests that the mean IQ score for subjects with medium lead levels is greater than for those with high lead levels. **Test Statistic:** Calculate the test statistic. (Round to two decimal places as needed.) **Visual Element:** - The image includes options for indicating null and alternative hypotheses, with option B being correctly marked. There is also a placeholder for calculating the
### Data on Lead Levels

#### Medium Lead Level Measurements:
- 72
- 94
- 92
- 85
- 83
- 97
- 83
- 92
- 104
- 111
- 91

#### High Lead Level Statistics:
- Sample size (\( n_2 \)): 11
- Mean (\( \bar{x}_2 \)): 89.356
- Standard deviation (\( s_2 \)): 10.454

This table presents measurements and statistical data for lead levels categorized into medium and high levels. The "Medium Lead Level" column lists individual measurements, while the "High Lead Level" section provides summary statistics.
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Transcribed Image Text:### Data on Lead Levels #### Medium Lead Level Measurements: - 72 - 94 - 92 - 85 - 83 - 97 - 83 - 92 - 104 - 111 - 91 #### High Lead Level Statistics: - Sample size (\( n_2 \)): 11 - Mean (\( \bar{x}_2 \)): 89.356 - Standard deviation (\( s_2 \)): 10.454 This table presents measurements and statistical data for lead levels categorized into medium and high levels. The "Medium Lead Level" column lists individual measurements, while the "High Lead Level" section provides summary statistics.
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